{"cells":[{"cell_type":"markdown","metadata":{"id":"3CCE088CD55B4EA48BFC04D8AAA3D66D","jupyter":{},"notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":" # <center>  Lecture 6 : MCMC </center>  \n \n##  <center>  Instructor: Dr. Hu Chuan-Peng   </center>  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"33A882665B1E46949937E06B4BC40B3B","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"在上一节课中，通过简单的 Beta-Binomial 模型中，我们已经看到 Stan可以帮助我们得到后验分布。  \n\n且这个过程中使用了**MCMC算法** 从后验分布中进行抽样。  \n\n为什么 **MCMC算法** 可以得到后验分布的样本？🤔  \n\n为了更深入理解这些方法，我们现在回到基础，从第一个MC(Monte Carlo)方法开始。😎  "},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"59B08AC6B6CD439CAFA1F4F01B8AE39D","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"## Monte Carlo, Markov Chain 和 Markov Chain Monte Carlo  \n\n### 什么是 Monte Carlo  \n\n- Monte Carlo 方法是一种通过**随机采样**模拟复杂现象的数值计算方法。  \n\n假设我们知道这个正方形的面积，想估算图中圆形的面积（但不使用圆的面积的公式），通过何种近似的方法可以怎么解决这一问题呢？  \n\n<center>  \n    <table>  \n            <tr>  \n                <td><img src=\"https://cdn.kesci.com/upload/slozv1v2pv.png?imageView2/0/w/480/h/960\" alt=\"\"></td>  \n                <td><img src=\"https://cdn.kesci.com/upload/slozv7t6h6.png?imageView2/0/w/480/h/960\" alt=\"\"></td>  \n            </tr>  \n            <tr>  \n                <td></td>  \n                <td></td>  \n            </tr>  \n    </table>  \n</center>  \n\n1. **随机投点**：我们在一个边长为 10厘米 的正方形区域内随机放置 20 个点。  \n2. **计算圆内的点数比例**：统计这些点中有多少落在圆内，并计算这一比例。  \n3. **面积估算**：根据比例，乘以正方形的面积（100 平方厘米），即可得到近似的圆面积。  \n\n**Monte Carlo 的核心思想**：  \n  1. **随机抽样**：通过从某个已知的概率分布中随机抽样，估计该分布的期望或其他统计量。  \n  2. **近似逼近**：随着样本数量增加，抽样结果会逐渐逼近真实分布的统计特性。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"6289BC6A1D034A97A40753E067F5A4B4","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"#### Normal-Normal 模型的后验分布  \n\n首先，以正态模型为例子（贝叶斯中，我们使用 Normal-Normal表示先验与似然都是正态分布）。  \n\n假设有一个标准差为0.75的正态分布，其均值$\\mu$未知，如何通过从该正态分布中抽取出的一个数据点($Y=6.25$)来估计其均值$\\mu$范围?  \n\n这个问题在贝叶斯的框架之下可以进行如下表述：  \n\n1. **似然模型**：平均值为$\\mu$，标准差为0.75的正态分布，从中抽取一个数据点$Y=6.25$：  \n    $$  \n    Y|\\mu  \\sim \\ N(\\mu, 0.75^2)  \n    $$  \n\n2. **先验模型**：上述正态分布的均值$\\mu$可能是从如下正态分布中取值的：  \n    $$  \n    \\mu  \\sim \\ N(0, 1^2)  \n    $$  \n\n    *可以简单理解为在看到$Y=6.25$这一数据点之前对$\\mu$的信念（$\\mu$在平均值为0，标准差为1的正态分布中波动*  ）  \n\n3. **后验分布**：那么在$Y=6.25$这个结果下，结合先验，更新后的$\\mu$是怎样的？  \n\n    $$  \n\t\t\\mu | (Y = 6.25) \\sim \\text{N}(?, ?)  \n\t\t$$  \n"},{"cell_type":"markdown","metadata":{"id":"4959BA5B744F4E0CA7F28C8973B5C25E","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"**后验分布的解析解：**  \n\n在第五课中，提示过Normal-Normal为共轭先验，因此其后验分布可直接计算：  \n\n$$  \n\\mu|\\vec{y} \\sim N\\left(\\frac{\\theta\\sigma^2 + \\bar{y}n\\tau^2}{n\\tau^2 + \\sigma^2}, \\frac{\\tau^2\\sigma^2}{n\\tau^2 + \\sigma^2}\\right)  \n$$  \n\n其中：  \n- $\\bar{y}$ 是样本的均值（观测到的数据, $Y=6.25$），  \n- $\\sigma^2$ 是数据的方差（此处用已知正态分布的方差0.75替代），  \n- $\\tau^2$ 是先验的方差（$\\sigma^2_{prior} = 1$）。  \n\n- **后验均值**：后验均值是先验均值 $\\theta$ 和样本均值 $\\bar{y}$ 的加权平均：  \n\n  $$  \n  \\text{posterior mean} = \\frac{0 \\times 0.75^2 + 6.25 \\times 1^2}{1^2 + 0.75^2} = \\frac{6.25}{1.5625} = 4  \n  $$  \n\n- **后验方差**：后验方差受先验的方差 $\\tau^2$ 和样本数据的方差 $\\sigma^2$ 的共同影响：  \n\n  $$  \n  \\text{posterior variance} = \\frac{1^2 \\times 0.75^2}{1^2 + 0.75^2} = \\frac{0.5625}{1.5625} = 0.6^2  \n  $$  \n \n> 因此，更新后的$\\mu$的分布为：  \n>  $\\mu | (Y = 6.25) \\sim \\text{N}(4, 0.6^2)$"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"9723A1A2449C4A49A3B35E769AA38051","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"在现代的概率编辑语言中，我们很容易能够进行Monte Carlo采样。  \n\n比如，对于上述的正态分布 $N(4, 0.6^2)$，将通过代码进行Monte Carlo采样并进行可视化。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"ACDB4B538C88433D85E58B84B0035061","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**后验分布模型 vs. 从后验分布采样**  \n\n📍需要明确的一点：通过解析计算得到的后验分布模型与从基于后验分布的采样结果并不完全相同。  \n\n在上述例子中，我们通过解析计算得到了后验分布的具体形式（模型）：  \n> $\\mu | (Y = 6.25) \\sim \\text{N}(4, 0.6^2)$  \n\n这并不意味着可直接从表达式中获得参数的**样本**。要生成这些样本，需要通过Monte Carlo过程采样。  \n\n简单地说：要得到的样本数量与每个样本在分布模型中的可能性之间是成比例的；某个值出现的概率越大，在采样中，它出现的次数应该越多。  \n\n反过来：如果能从某个分布中采到足够多的符合分布模型的样本，则可通过对样本的统计量的计算来估计该分布本身的模型参数。"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"116032831ECE4825A9B316D37969B13C","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 安装和加载包\noptions(repos = c(CRAN = \"https://mirrors.tuna.tsinghua.edu.cn/CRAN/\"))\nif (!requireNamespace('pacman', quietly = TRUE)) {\n    install.packages('pacman')\n}\npacman::p_load(\"tidyverse\",\"ggplot2\", \"dplyr\",\"gridExtra\",\"papaja\", \"patchwork\",\"bayesplot\",\"rstan\")\noptions(warn = -1)  # 抑制警告","outputs":[],"execution_count":1},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"C06719EBE45A41BE978A87A0CFA4F123","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 设置 x 的范围为 [2, 10]\nx_range <- seq(2, 10, length.out = 1000)\n\n# 计算正态分布的概率密度函数\ny_norm <- dnorm(x_range, mean = 6.25, sd = 0.75)\n\n# 对正态分布进行采样，得到1000个样本值\nsamples <- rnorm(1000, mean = 6.25, sd = 0.75)\n\n# 显示前 10 个样本值\ncat(\"前 10 个样本值：\", head(samples, 10))","outputs":[{"output_type":"stream","name":"stdout","text":"前 10 个样本值： 6.686012 6.411216 6.769499 7.49096 6.522845 5.554819 6.847993 5.694025 7.064686 6.400447"}],"execution_count":2},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"4EEF6C371CBA49298E7BE90A4FA21ABC","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 绘制图像\noptions(repr.plot.width=10, repr.plot.height=6) \ndf <- data.frame(x = x_range, y = y_norm)\nggplot2::ggplot(df, aes(x = x, y = y)) +\n  ggplot2::geom_histogram(aes(x = samples, y = ..density..),  \n                          bins = 45, \n                          fill = \"lightgrey\", \n                          color = \"black\") +\n  ggplot2::geom_line(color = 'red', size = 1.5)+ \n  ggplot2::scale_y_continuous(expand = c(0, 0) , limits = c(0, 0.55)) +\n  papaja::theme_apa()","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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e/e+GffyT08/e/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src=\"https://cdn.kesci.com/upload/rt/4EEF6C371CBA49298E7BE90A4FA21ABC/t4h8qdy4n8.svg\">"},"metadata":{"image/png":{"width":600,"height":360},"image/jpeg":{"width":600,"height":360},"image/svg+xml":{"width":600,"height":360,"isolated":true},"application/pdf":{"width":600,"height":360}}}],"execution_count":3},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"7A27BDC05F214F1E9A76116662313C3B","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**未归一化的后验分布(unnormalized posterior pdf)**  \n\n上节课讲到，在现实的数据分布中，往往模型比较复杂，导致计算变得复杂，尤其是分母部分的归一化因子。  \n\n❓为什么归一化因子比较难以计算？  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"E1EFA6CB380C41D2B34B45CEFCDFF580","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"假如归一化因子（分母）比较难以计算，是不是可以不计算？  \n\n<center>  \n    <table>  \n            <tr>  \n                <td><img src=\"https://cdn.kesci.com/upload/slozv1v2pv.png?imageView2/0/w/480/h/960\" alt=\"\"></td>  \n                <td><img src=\"https://cdn.kesci.com/upload/slozv7t6h6.png?imageView2/0/w/480/h/960\" alt=\"\"></td>  \n            </tr>  \n            <tr>  \n                <td></td>  \n                <td></td>  \n            </tr>  \n    </table>  \n</center>  \n\nQ: 假如只知道上面随机点的信息，但不知道正方形的面积，如何估算圆的面积？  \nA: 使用足够多的点，计算圆内点的比例"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"5DE09A4C24D74324BA32C0EB1A25D4E2","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"对于贝叶斯推断来说，可以不用计算归一化因子，直接通过对后验分布的采样来近似得到后验分布。  \n\n$$  \nf(\\mu | y=6.25) \\propto f(\\mu)L(\\mu|y=6.25)  \n$$  \n\n- 尽管未归一化的分布并不是真正的后验分布，但这二者的形状、集中趋势、变异性是一样的  \n- 可以看到，真实的后验分布和未归一化后验分布，处理在 y 轴上的单位不一样，但他们的形状、集中趋势、变异性是一样的  \n- 重要的是，两个分布中，$\\mu$ 的结果主要集中在 2-6 之间  \n\n因此，当进行采样时，可以使用**未归一化的后验分布** 的结果来替代计算真实的后验分布 $f(\\mu)$  \n\n![Image Name](https://cdn.kesci.com/upload/s2ty9jty8t.png?imageView2/0/w/960/h/960)  \n\n\n那么新的问题是，如何在不计算复杂归一化常数的情况下，有效地生成样本？🤔  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"C4589C673DE34CE4B5888F01EE7A404E","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### Markov Chain Monte Carlo  \n\nMarkov Chain（马尔可夫链）即可自然地解决了未归一化的后验分布的问题。  \n\n原因：  \n- 每次只关注当前的状态。  \n- 利用当前状态生成建议分布（proposed distribution）。  \n- 判断是否接受新的状态，构建一个链条来近似后验分布。  \n\n以一个心情变化的例子来深入理解 Markov Chain：  \n\n- 假如不同的情绪对应一种状态，也就是参数可能的取值。  \n- 那么，我们可以将不同的心情（如“冷静”、“悲伤”、“开心”）定义为 状态。这些状态中的每一个代表参数 $\\theta_k$ 的不同取值：  \n  - 例如，冷静是 $\\theta_1=0.5$; 悲伤是 $\\theta_2=0.3$；开心是$\\theta_3=0.7$； 以此类推.....。  \n  - 这样，我们可以确定参数选择的范围 $\\theta_{k} \\sim [0,1]$，参数是离散变量，每一个值对应一种心情。  \n  - 注意，我们用下标 k 来表示不同的心情以及对应的参数值。  \n\n<table>  \n    <tr>  \n        <td><img src=\"https://cdn.kesci.com/upload/s2vta0gekr.png?imageView2/0/w/500/h/500\" alt=\"图片1\" width = 600></td>  \n    </tr>  \n</table>  \n\n- 状态转移：每一天我们的心情都会发生变化或者不变，代表一次采样，即一次状态的转移。  \n   - 长时间跟踪这些状态，我们会得到一个 马尔可夫链:$\\left\\lbrace \\theta^{(1)}, \\theta^{(2)}, \\ldots, \\theta^{(N)} \\right\\rbrace$,这里 $n$ 表示天数，$\\theta^{(n)}$ 是第 $n$ 天的具体心情。  \n\n- **“无记忆性”**：无记忆性是马尔可夫链的关键特点,今天的心情（当前状态）只依赖于昨天的心情（前一状态），例如：  \n   - 如果前一天是“开心” $\\theta_3$，那么今天仍然保持“开心”的概率是 0.5，  \n   - 变为“冷静”的概率是 0.25，变为“悲伤”的概率也是 0.25。"},{"cell_type":"markdown","metadata":{"id":"888D39A34C1141FA97371983E8270F25","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"\n我们可以根据上面的概率构建一个状态转移表，用于描述从一个状态跳转到另一个状态的可能性：  \n\n| 心情 | 开心$\\theta^{(n)}_{1}$ | 冷静$\\theta^{(n)}_{2}$ | 悲伤$\\theta^{(n)}_{3}$ | ... |  \n| :----: | :----: | :----: | :----: | :----: |  \n| 开心$\\theta^{(n-1)}_{1}$ | 0.5 | 0.25 | 0.25 | ... |  \n| 冷静$\\theta^{(n-1)}_{2}$ | 0.5 | 0 | 0.5 | ... |  \n| 悲伤$\\theta^{(n-1)}_{3}$ | 0.25 | 0.25 | 0.5 | ... |  \n| ... | ... | ... | ... | ... |  \n\n解释：  \n- 每一行代表当前状态影响下一状态的概率，也就是 当日心情(n)受到上一天心情(n-1)的影响。  \n- 可以写成服从概率分布的形式：$choice(n) \\sim Distribution(n-1)$。  \n- 这里的 **Distribution 可以理解为建议分布**。  \n  - 它为第二天的心情变化提供了可能的选项，所以被称为建议分布 $q(x)$，并且根据这个分布来选择是否接受新的状态。  \n  \n马尔可夫链的的好处：当我们运行一段时间后，会发现慢慢会稳定在某个状态，高概率的更多出现，低概率的情况更少出现。  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"7164BBD80EB0457CA64AEF0FB55D59C5","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 为什么 Monte Carlo 需要加上 Markov Chain？  \n\n原因：  \n1. Monte Carlo 方法通过从目标分布中直接采样，使用大量随机样本来逼近期望值或目标概率。这种方法在低维分布中工作良好，但在高维复杂分布中直接采样变得非常困难和不现实。  \n\n2. 为了解决高维空间中的采样困难，MCMC 使用马尔可夫链生成样本。每次样本的生成只依赖于前一次的状态，因此构建了一个可以逐渐收敛于目标分布的链条。  \n\n所以，MCMC 的核心思想即：  \n- **构建一个符合目标分布的马尔可夫链**：  \n每次新样本的生成依赖于前一个状态，逐步逼近目标分布。  \n- **长时间采样达到平稳分布**：  \n当马尔可夫链达到稳态分布时，采样结果便可以作为目标分布的近似。  \n\n尽管 MCMC 的实现方式多种多样，但所有方法的目标都是构建一个符合目标后验分布的马尔可夫链。许多 MCMC 算法，如 **吉布斯采样**、**差分进化算法** 以及 PyMC 默认使用的 **NUTS**（No-U-Turn Sampler），都是 **Metropolis-Hastings** 算法的变种。  \n    \n<table>  \n        <tr>  \n            <td><img src=\"http://gorayni.github.io/assets/posts/gibbs/gibbs2.gif\" alt=\"\" width=\"200\" height=\"200\"></td>  \n            <td><img src=\"https://matteding.github.io/images/diff_evol.gif\" alt=\"\" width=\"200\" height=\"200\"></td>  \n            <td><img src=\"https://cdn.kesci.com/upload/image/rjvh3zx4an.gif?imageView2/0/w/640/h/640\" alt=\"\" width=\"200\" height=\"200\"></td>  \n        </tr>  \n        <tr>  \n            <td>吉布斯采样算法</td>  \n            <td>差分进化算法</td>  \n            <td>汉密尔顿算法</td>  \n        </tr>  \n</table>  \n\n\n通过这些算法，我们可以对难以直接求解的后验分布进行近似。  \n\n我们将在本节课重点讨论 Metropolis-Hastings (MH) 算法，而不是研究所有的变种。  \n\n- 虽然实现该算法需要计算机编程技能，而这些技能并不在本课程的范围之内（例如编写函数和 for 循环），    \n- 😜ps. 即使没有学会 MH 算法的实现，也不妨碍我们通过 stan 来实现各种 MCMC 算法。  "},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"F2E061797A0847C8B5DA6175CF5EE9A9","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"## Metropolis-Hastings(MH)算法  \n\n上面的例子已经涉及到 MH 算法最朴素的思想：  \n\n- 根据后验模型 y 轴的大小(概率密度)来决定 x 轴参数的数量。  \n  - 首先，均匀的从参数范围($x~[0,1]$)中抽取 10000个参数样本 $\\mu_i$。  \n  - 然后，对于每个 $\\mu_i$ 计算其在后验分布中的概率密度值 $f(\\mu_i)$ 的大小，$f(\\mu_i)$ 越大则 $\\mu_i$ 被保留的可能性越高。   \n- 但通常计算 $f(\\mu_i)$ 是比较困难的，我们可以计算非标准化的 $f(\\mu_i)$。  \n- 此外，在[0,1]中进行均匀采样的做法效率太低，可利用 MCMC 状态转移的性质来提高采样效率。  \n\n现在我们就来体验这个奇妙的过程。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0D3567C936C5426C93F24C88777A2C07","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 建议分布(proposed distribution)  \n\n为了提高采样效率，通常**不会**直接从某个分布中大量采样，再进行筛选(也被称为拒绝)，这种方式可能效率非常低。  \n\n在MCMC 中，首先构建建议分布 (proposed distribution) $q(x)$，然后利用 MCMC 状态转移的性质来进行采样。  \n\n通过建议分布，我们可以在 MCMC 的状态转移过程中构造出一条马尔可夫链。这条链最终会收敛于目标后验分布，使得生成的样本接近真实的目标分布。  \n\n在刚才所讲的心情状态的变化过程实际上就是一个建议分布的例子。  \n\n>  \n![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch-7-mh-proposal-1.png)  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"01DA13360EC7428B81AC14EF83E8D198","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"接下来，需要了解**如何根据建议分布进行采样**，以及如何从 **建议分布 $q(x)$ 得到后验分布 $p(x)$** 。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"3A3AD59D82B04C94BCA8D612200C0901","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 接受率 (acceptance probability)  \n\n当前样本可根据上一个样本从建议分布中进行采样 $\\theta^{n} \\sim Normal(\\theta^{n-1}_{k},\\sigma)$。  \n\n但应该如何判断当前的采样是否合理？换句话说，保留还是拒绝当前所采的样本数据。  \n- 假设上一次采样的参数值为 $\\theta^{n-1} = 3$， 根据建议分布$q(\\theta) = Normal(3, 1)$ 进行一次采样，得到参数 $\\theta^{n} = 1$。  \n- 假定后验分布(或者未标准化的后验分布)为 $p(\\theta) = Normal(5,1)$。  \n- 显然，$\\theta^{n} = 1$ 在 $p(\\theta)$ 的边缘。那我们是否要保留该采样呢？"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"F1846146434945E68A4E4DCCA995DBA0","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**不同接受策略的影响**  \n\n* 可以考虑三种接受建议的情况：  \n\n    1：始终不接受提议。  \n\n    2：始终接受提议。  \n\n    3：只有当提议(n+1)的后验可能性大于当前(n)值的后验可能性时，才接受提议  \n\n* 看看这三种情况对应生成的trace plot  \n![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch7-bad-step2-1.png)  \n\n    A. 使得马尔科夫链在采样时一直停在同一个值  \n\n    B. 马尔科夫链的采样并不会稳定在某一个范围内  \n    \n    C. 采样只停留在$\\mu = 4$附近(只能采到一部分值)  \n\n* 因此，尽管采样应该更多地停留在“高后验可能性的值”，但也不能只取到这附近的值。  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"9D3B0A445CBE43AAB812A038DA423538","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**接受率 (acceptance probability)**  \n\n“采样应该更多地停留在'高后验可能性的值'，但也不能只取到这附近的值”，意味着需要选择一个合适的接受策略。  \n\n--> 接受率 ($\\alpha$, acceptance probability)就是为了解决这个问题。  \n\n- 首先，我们将从建议模型中抽取一个新的参数 $\\theta^{n+1}$ 的概率为 $q(\\theta^{n+1}|\\theta^{n})$  \n- 对于是否接受 $\\theta^{n+1}$，我们定义接受概率$\\alpha$  \n$$  \n  \\alpha = \\min\\left\\lbrace 1, \\; \\frac{f(\\theta^{n+1})L(\\theta^{n+1}|y)}{f(\\theta^{n})L(\\theta^{n}|y)} \\times \\frac{q(\\theta^{n}|\\theta^{n+1})}{q(\\theta^{n+1}|\\theta^{n})} \\right\\rbrace.  \n$$  \n- 别看这公式很复杂，其实很简单。  \n- 分数的上下分别代表下一个参数$\\theta^{n+1}$和当前参数$\\theta^{n}$的非标准化后验。即我们之前提到，要通过非标准化后验来判断是否接受一个参数。  \n  - 其中，$f(\\theta)L(\\theta|y)$ 为非标准化后验  \n  - $q(\\theta^{n}|\\theta^{n+1})$ 部分代表了从建议分布中采样新参数的过程。  \n- 可以想象，$\\frac{f(\\theta^{n+1})L(\\theta^{n+1}|y)}{f(\\theta^{n})L(\\theta^{n}|y)}$ 大于1且其值越大，表明下一个参数$\\theta^{n+1}$的后验概率越大，因此它越有可能被接受。  \n- 如果$\\frac{f(\\theta^{n+1})L(\\theta^{n+1}|y)}{f(\\theta^{n})L(\\theta^{n}|y)}$小于1，则代表下一个参数$\\theta^{n+1}$的后验概率过小，因此我们要舍弃它。  \n\n所以，对于是否接受或拒绝新的参数 $\\theta^{n+1}$，则有：  \n$$  \n\\theta^{(n+1)} =  \n \\begin{cases}  \n \\theta^{(n+1)} &  \\text{ with probability } \\alpha \\\\  \n \\theta^{(n)} &  \\text{ with probability } 1- \\alpha. \\\\  \n \\end{cases}  \n $$  \n- 也就是如果我们不接受新的参数，那我们用原来的参数替代现在的参数。  \n- 这样避免了参数采样被浪费，并且使得概率更大的参数被更多的采样。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"C2B7FA80A3004CCBBC8EEBA33645C063","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"总的来说，MH 算法包含两个关键思想和两个关键步骤：  \n\n两个关键思想  \n- 根据非标准化的后验进行参数的接受或拒绝  \n- 根据 MCMC 的特性设置建议分布来完成状态转移  \n\n两个关键步骤  \n- 设定建议分布  \n- 根据建议分布的参数、未标准化后验计算接受率"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"A23688B4D6264D6BB64FEFA17A641A8B","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 代码示例  \n\n我们使用代码感受一下这个过程"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"1E1801584A5D4CB58E2BDB4A63186EC0","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"首先，我们假设当前的参数值 $\\theta^{n} = 3$，然后我们根据该参数设定建议分布，并进行一次新的采样。  \n\n- 注意，为了方便演示，我们将建议分布(正态分布)的 $\\sigma$ 固定为1。"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"130F77AAA88248859E31EBA7A8DE1D6F","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"set.seed(2024)\n\ncurrent <- 3                                  # 假设theta^n为3\n\nproposal <- rnorm(1, mean = current, sd = 1)  # 从当前正态分布中抽出一个样本作为建议分布的mu\n\ncat(\"从建议分布中新采样 θ(n+1)为：\", proposal)","outputs":[{"output_type":"stream","name":"stdout","text":"从建议分布中新采样 θ(n+1)为： 3.981969"}],"execution_count":4},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"3ED70E58B8C643CB94912BB894A85A89","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"接着，我们根据新采样得到的参数计算其相关的接受率。  \n- 注意，假定先验为正态分布：$N(\\mu = 3, \\sigma = 1)$  \n- 另外，假设似然模型仅包含一个数据：$Y = 6$"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"9972ADFB8B55409FACE0AF35C150D3E6","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 设置先验\nproposal_prior <- dnorm(proposal, mean = 3, sd = 1)  # 先验概率密度\ncurrent_prior <- dnorm(current, mean = 3, sd = 1)    # 先验概率密度\n\n# 定义似然函数\nlikelihood <- function(theta) {\n  Y <- 6  # 假设数据 Y 为 6\n  return(dnorm(Y, mean = theta, sd = 0.75))  # 固定 sd=0.75\n}\n\n# 计算建议位置的未归一化的后验概率值（先验 * 似然）\nproposal_posterior <- proposal_prior * likelihood(proposal)\n\n# 计算当前位置的未归一化的后验概率值（先验 * 似然）\ncurrent_posterior <- current_prior * likelihood(current)\n\n# 计算接受概率α，为两者概率值之比\nalpha <- min(1, proposal_posterior / current_posterior)\n\n# 打印出接受概率α\ncat(\"后验比为：\", proposal_posterior / current_posterior, \", alpha为:\", alpha, \"\\n\")","outputs":[{"output_type":"stream","name":"stdout","text":"后验比为： 49.29954 , alpha为: 1 \n"}],"execution_count":5},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0549A0B206D94AC885F2450E1AA4007F","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"最后，我们根据接受率 $\\alpha$来决定是否接受建议分布的参数作为新的采样值。"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"B82533C5AAC8481CA5E02672222C6D98","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 根据接受概率α进行抽样，抽样内容为建议位置和当前位置\nnext_stop <- sample(c(proposal, current), 1, prob = c(alpha, 1 - alpha))\n\n# 打印出下一个位置的值\ncat(\"下一个位置的值为:\", next_stop, \"\\n\")\n# 从第一段代码我们可以看到此时的接受概率α=1，因此接受了建议值作为我们的下一个值","outputs":[{"output_type":"stream","name":"stdout","text":"下一个位置的值为: 3.981969 \n"}],"execution_count":6},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0025DF9A1BA1467B9E2936C36C12B3BE","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**定义单次采样函数**  \n\n我们可以直接定义一个函数，将刚刚的操作全都结合在一起，这样当我们想进行抽样的时候，不用重复写代码"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"3A6E114306F44F97A2113DF015CD3913","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"one_mh_iteration <- function(current, sigma = 1) {\n  \n  # 提议值:从均值为current，方差为sigma（默认值为1）的正态分布中抽样\n  proposal <- rnorm(1, mean = current, sd = sigma)\n  \n  # 设置先验并计算概率密度\n  proposal_prior <- dnorm(proposal, mean = 3, sd = 1)  # 先验概率密度\n  current_prior <- dnorm(current, mean = 3, sd = 1)  # 先验概率密度\n \n  \n  # 定义似然函数\n  likelihood <- function(theta) {\n    Y <- 6  # 假设数据 Y 为 6\n    return(dnorm(Y, mean = theta, sd = 0.75))  # 计算似然\n  }\n  \n  # 计算未归一化的后验概率\n  proposal_posterior <- proposal_prior * likelihood(proposal)\n  current_posterior <- current_prior * likelihood(current)\n  \n  # 计算接受概率 alpha\n  if (is.na(proposal_posterior) || is.na(current_posterior) || current_posterior <= 0) {\n    alpha <- 0\n  } else {\n    alpha <- min(1, proposal_posterior / current_posterior)\n  }\n    \n  # 根据接受概率 alpha 进行抽样\n  next_stop <- sample(c(proposal, current), 1, prob = c(alpha, 1 - alpha), replace = TRUE)\n                      \n  # 返回建议值、接受概率和下一个位置组成的数据框\n  result <- data.frame(proposal = proposal, alpha = alpha, next_stop = next_stop)\n                      \n  return(result)\n}\n\n# 设置随机种子\nset.seed(2024)\n\n# 调用函数并显示结果\nresults <- one_mh_iteration(current = 3)\nprint(results, row.names = FALSE) ","outputs":[{"output_type":"stream","name":"stdout","text":" proposal alpha next_stop\n 3.981969     1  3.981969\n"}],"execution_count":7},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"AF0F034BD1E9461685DFCCDCD32F0BA8","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 变换不同的随机数种子，其实也是生成不同的建议值\nset.seed(83)\n\n# 调用函数并显示结果\nresults <- one_mh_iteration(current = 3)\nprint(round(results, digits = 4), row.names = FALSE) #用round对数据框内数字四舍五入，保留4位小数","outputs":[{"output_type":"stream","name":"stdout","text":" proposal alpha next_stop\n   0.6258     0         3\n"}],"execution_count":8},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"06FBC3E2AD2A4E94B027B6672DB1B480","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**多次采样**  \n\n上述函数只进行了一次采样，即当前位置为3时，下一个可能采样的结果  \n\n基于当前位置，提出下一个采样值，接受或拒绝它。那么新的采样值就变成了当前位置，我们需要不断重复这个过程"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"58C6F9CEE726436F953043BBC23C7B09","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"mh_tour <- function(N, sigma = 1) {\n  current <- 3\n  mu <- numeric(N)  # 创建一个长度为 N 的零向量\n\n  # 循环进行 N 次迭代\n  for (i in 1:N) {\n    sim <- one_mh_iteration(current, sigma)  # 调用采样函数\n    mu[i] <- sim$next_stop  # 保存当前的下一个位置\n    current <- sim$next_stop  # 更新当前值\n  }\n\n  # 返回包含迭代次数和每次采样结果的数据框\n  result <- data.frame(iteration = 1:N,mu = mu)\n  \n  return(result)\n}","outputs":[],"execution_count":9},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"1940339DBF964334B5D9C774D2A5DF07","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 调用定义好的函数，将采样次数设为5000\nset.seed(84735)\nmh_simulation <- mh_tour(N=5000)\ntail(mh_simulation, n = 5)","outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 5 × 2</caption>\n<thead>\n\t<tr><th></th><th scope=col>iteration</th><th scope=col>mu</th></tr>\n\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>4996</th><td>4996</td><td>5.435994</td></tr>\n\t<tr><th scope=row>4997</th><td>4997</td><td>5.435994</td></tr>\n\t<tr><th scope=row>4998</th><td>4998</td><td>4.784854</td></tr>\n\t<tr><th scope=row>4999</th><td>4999</td><td>4.200179</td></tr>\n\t<tr><th scope=row>5000</th><td>5000</td><td>4.200179</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 5 × 2\n\n| <!--/--> | iteration &lt;int&gt; | mu &lt;dbl&gt; |\n|---|---|---|\n| 4996 | 4996 | 5.435994 |\n| 4997 | 4997 | 5.435994 |\n| 4998 | 4998 | 4.784854 |\n| 4999 | 4999 | 4.200179 |\n| 5000 | 5000 | 4.200179 |\n\n","text/latex":"A data.frame: 5 × 2\n\\begin{tabular}{r|ll}\n  & iteration & mu\\\\\n  & <int> & <dbl>\\\\\n\\hline\n\t4996 & 4996 & 5.435994\\\\\n\t4997 & 4997 & 5.435994\\\\\n\t4998 & 4998 & 4.784854\\\\\n\t4999 & 4999 & 4.200179\\\\\n\t5000 & 5000 & 4.200179\\\\\n\\end{tabular}\n","text/plain":"     iteration mu      \n4996 4996      5.435994\n4997 4997      5.435994\n4998 4998      4.784854\n4999 4999      4.200179\n5000 5000      4.200179"},"metadata":{}}],"execution_count":10},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0D1F55C63DAE466F9DA291D031EC0FD4","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**采样结果图示**"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"ADE65C328EAF473CAFEEB54D7A59F39A","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 绘制密度图\ndensity_plot <- ggplot2::ggplot(mh_simulation, aes(x = mu)) +\n  ggplot2::geom_histogram(aes(y = ..density..), \n                 bins = 30, \n                 color = \"white\", \n                 fill = \"darkgrey\", \n                 alpha = 0.7) +\n  ggplot2::geom_density(aes(y = ..density..), \n               color = \"#6497b1\", \n               size = 1) +\n  ggplot2::labs(x = \"mu\", y = \"density\") +\n  papaja::theme_apa()  + \n  ggplot2::scale_y_continuous(expand = c(0, 0) , limits = c(0, 0.7)) \n\n# 绘制轨迹图\ntrace_plot <- ggplot2::ggplot(mh_simulation, aes(x = iteration, y = mu)) +\n  ggplot2::geom_line(color = \"#6497b1\") +\n  ggplot2::labs(x = \"iteration\", y = \"mu\") +\n  papaja::theme_apa()  + \n  ggplot2::scale_y_continuous(limits = c(3, 9)) \n\n# 将两个图并排显示\noptions(repr.plot.width=16, repr.plot.height=7) \ndensity_plot + trace_plot\n","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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ey6xME8YY3geRk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\nrcgz42vnrcBj51P3jDc1jcTGv7zwxum3j79MOlxBsYin/WaBdLhR8qaa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src=\"https://cdn.kesci.com/upload/rt/ADE65C328EAF473CAFEEB54D7A59F39A/t4h8qfm06o.svg\">"},"metadata":{"image/png":{"width":960,"height":420},"image/jpeg":{"width":960,"height":420},"image/svg+xml":{"width":960,"height":420,"isolated":true},"application/pdf":{"width":960,"height":420}}}],"execution_count":11},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"098C1DC8DA5D4B3EAA37E207F24F708D","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"我们可以使用 bayesplot包简化这个绘图的过程"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"1B7292D190764C23A71504E3D12B8213","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"#创建绘图数据框\nsample <- as.data.frame(mh_simulation$mu)\n\n#采样密度图\ndens <- bayesplot::mcmc_dens(sample) +    \n        ggplot2::labs(x = \"mu\", y = \"density\") +\n        papaja::theme_apa()\n\n#采样轨迹图\ntrace <- bayesplot::mcmc_trace(sample) +  \n        ggplot2::labs(x = \"iteration\", y = \"density\") +\n        papaja::theme_apa()\n\ndens + trace","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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Os/ROs/ROs/ROs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\nXsm+b1g+Rn6ge43mzejKCWuS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AwIDAg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\nNzQ2CiUlRU9GCg==","text/html":"<img src=\"https://cdn.kesci.com/upload/rt/1B7292D190764C23A71504E3D12B8213/t4h8qgs1wj.svg\">"},"metadata":{"image/png":{"width":960,"height":420},"image/jpeg":{"width":960,"height":420},"image/svg+xml":{"width":960,"height":420,"isolated":true},"application/pdf":{"width":960,"height":420}}}],"execution_count":12},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"A1AA674552224BF78C326668A1749650","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 调试(Tuning)Metropolis-Hastings 算法  \n\n在建议分布 $\\mu_{n+1} | \\mu_{n} \\; \\sim \\; \\text{Normal}(\\mu_{n}, \\sigma)$中，$\\sigma$反映了 建议选项的分布宽度，对$\\sigma$ 的选择也会影响马尔科夫链的表现  \n\n🧐思考：我们仍然使用MH算法，尝试三种不同的$\\sigma$  \n* $\\sigma = 0.01$  \n* $\\sigma = 1$  \n* $\\sigma = 100$  \n    \n请你判断以下的轨迹图和密度图分别对应上述哪种情况  \n\n![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch7-bad-idea-1.png)  \n\n\n可以结合以下代码进行判断"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"6B2D72E99E5842AD8DC848271C2FBDE3","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"one_mh_iteration <- function(current, sigma = 1) {\n  \n  # 提议值:从均值为current，方差为sigma（默认值为1）的正态分布中抽样\n  proposal <- rnorm(1, mean = current, sd = sigma)\n  \n  # 设置先验并计算概率密度\n  proposal_prior <- dnorm(proposal, mean = 3, sd = 1)\n  current_prior <- dnorm(current, mean = 3, sd = 1)  \n  \n  # 定义似然函数\n  likelihood <- function(theta) {\n    Y <- 6  # 假设数据 Y 为 6\n    return(dnorm(Y, mean = theta, sd = 0.75))  # 计算似然\n  }\n  \n  # 计算未归一化的后验概率\n  proposal_posterior <- proposal_prior * likelihood(proposal)\n  current_posterior <- current_prior * likelihood(current)\n  \n  # 计算接受概率 alpha\n  if (is.na(proposal_posterior) || is.na(current_posterior) || current_posterior <= 0) {\n    alpha <- 0\n  } else {\n    alpha <- min(1, proposal_posterior / current_posterior)\n  }\n    \n  # 根据接受概率 alpha 进行抽样\n  next_stop <- sample(c(proposal, current), 1, prob = c(alpha, 1 - alpha), replace = TRUE)\n                      \n  # 返回建议值、接受概率和下一个位置组成的数据框\n  result <- data.frame(proposal = proposal, alpha = alpha, next_stop = next_stop)\n                      \n  return(result)\n}\n\nmh_tour <- function(N, sigma = 1) {\n  current <- 3\n  mu <- numeric(N)  # 创建一个长度为 N 的零向量\n\n  # 循环进行 N 次迭代\n  for (i in 1:N) {\n    sim <- one_mh_iteration(current, sigma)  # 调用采样函数\n    mu[i] <- sim$next_stop  # 保存当前的下一个位置\n    current <- sim$next_stop  # 更新当前值\n  }\n\n  # 返回包含迭代次数和每次采样结果的数据框\n  result <- data.frame(iteration = 1:N,mu = mu)\n  \n  return(result)\n}","outputs":[],"execution_count":13},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"D56C72A31919408E9D4B1B70515F4047","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"#===========================================================================\n#                            请修改 sigma 的值。\n#===========================================================================\nset.seed(84735)\nmh_simulation = mh_tour(N=5000, sigma=1)\n#创建绘图数据框\nsample_x <- as.data.frame(mh_simulation$mu)\n\n#采样密度图\ndens_x <- bayesplot::mcmc_dens(sample_x) +    \n        ggplot2::labs(x = \"mu\", y = \"density\") +\n        papaja::theme_apa()\n\n#采样轨迹图\ntrace_x <- bayesplot::mcmc_trace(sample_x) +  \n        ggplot2::labs(x = \"iteration\", y = \"density\") +\n        ggplot2::scale_y_continuous(limits = c(2.5, 9)) +\n        papaja::theme_apa()\n\ndens_x + trace_x","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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+wNsFPsPZPsPZP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\nTGVuZ3RoMSA5Mjg0Cj4+CnN0cmVhbQp4nN06e3wU1dX3zMy+8pp9Z5IN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src=\"https://cdn.kesci.com/upload/rt/D56C72A31919408E9D4B1B70515F4047/t4h8rcvudf.svg\">"},"metadata":{"image/png":{"width":960,"height":420},"image/jpeg":{"width":960,"height":420},"image/svg+xml":{"width":960,"height":420,"isolated":true},"application/pdf":{"width":960,"height":420}}}],"execution_count":13},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"C3E5B9EC17904341AF6C4F9002EA236D","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"#===========================================================================\n#                            可以自行复制代码多试几次\n#===========================================================================\nmh_simulation = mh_tour(N=5000, sigma=...)\n#创建绘图数据框\nsample_x <- as.data.frame(mh_simulation$mu)\n\n#采样密度图\ndens_x <- bayesplot::mcmc_dens(sample_x) +    \n        ggplot2::labs(x = \"mu\", y = \"density\") +\n        papaja::theme_apa()\n\n#采样轨迹图\ntrace_x <- bayesplot::mcmc_trace(sample_x) +  \n        ggplot2::labs(x = \"iteration\", y = \"density\") +\n        ggplot2::scale_y_continuous(limits = c(2.5, 9)) +\n        papaja::theme_apa()\n\ndens_x + trace_x","outputs":[],"execution_count":16},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"BE6757F1E6D44F8F8D9B07578C32AC17","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"**总结**  \n\n* 当$w = 0.01$时：  \n\n    建议分布的范围很窄，比如$Normal(3, 0.01)$，这会导致下一个建议值和当前值非常接近，则$f(\\mu')L(\\mu'|y) \\approx f(\\mu)L(\\mu|y)$  \n    $$  \n    \\alpha = \\min\\left\\lbrace 1, \\; \\frac{f(\\mu')L(\\mu'|y)}{f(\\mu)L(\\mu|y)} \\right\\rbrace \\approx \\min\\left\\lbrace 1, \\; 1 \\right\\rbrace \\; = 1  \n    $$  \n    那么我们很容易接受下一个采样值，但尽管马尔科夫链一直在转移，但探索的范围太窄了，我们可以看到采样一直在3附近  \n\n* 当$w = 100$时：  \n\n    类似的，我们可以推知此时建议分布的范围太宽了，超出了$\\mu$可能的取值  \n\n    下一个建议值和当前值间隔太远，这会导致我们经常拒绝下一个采样值，多次停在当前位置。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"56BB1356EF1B41E48F642AF3621E307A","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 小结  \n\n无论是在这些相对简单的单参数模型设置中，还是在更复杂的模型设置中，Metropolis-Hastings 算法都是通过两步之间的迭代，从后验中产生近似样本：  \n- 设定建议分布  \n- 根据建议分布的参数、未标准化后验计算接受率  \n\n本节课我们只考虑了一种 MCMC 算法，即 Metropolis-Hastings。这种算法虽然功能强大，但也有其局限性。  \n- 在以后的章节中，贝叶斯模型的参数会大大增加，手动调整 Metropolis-Hastings 算法以充分探索每个参数的空间会变得很繁琐。  \n- 然而，即使 Metropolis-Hastings 算法的实用性达到了极限，它仍然是一套更灵活的 MCMC 工具的基础，包括自适应 Metropolis-Hastings、Gibbs 和 Hamiltonian Monte Carlo (HMC) 算法。其中，HMC 是 stan 和 PyMC 默认使用的算法。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"C0435BBAE2BE416EAEE0EEFEBA6F9EB0","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"## Stan实战  \n\n在上一部分，我们学习了 MCMC 算法的基本原理，并通过 R 代码实现了一次简单的 Metropolis-Hastings 迭代。  \n但随着模型复杂性提升，我们发现手动实现 MCMC 代码可能会变得非常繁琐.  \n\n同时在第五课中，我们使用网格法对 Beta-Binomial 模型进行了推断，并初步介绍了 Stan。  \n下面我们会深入讲解如何利用 Stan，借助 MCMC 方法进行高效的贝叶斯推断。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"D152FD05A6A94DD8AC81DF45767A9952","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 为什么选择Stan？  \n\n* **灵活的操作**：Stan 提供了一种用户友好的界面，使得模型定义过程相对简单，用户可以灵活地使用 Stan 的建模语言来定义复杂的贝叶斯模型。  \n* **活跃的社区**：Stan 拥有一个活跃的用户社区，提供丰富的资源、教程和文档，方便新手学习和解决问题。  \n\n接下来我们介绍 Stan 的基本使用流程和核心模块。  \n1. **模型定义**：Stan 中用户可以通过`model`部分定义先验分布和似然函数，构建完整的统计模型。  \n2. **概率分布（Distributions）**：Stan 支持多种常见的概率分布，例如 Normal, Beta, Bernoulli, Binomial, Poisson 等。  \n3. **采样（Sampling）**：Stan 使用多种采样算法进行后验采样,如Metropolis-Hastings和NUTS（No-U-Turn Sampler）。  \n4. **后验预测**：Stan 支持从后验分布生成新的观测值，根据`generated quantities`它可以帮助我们验证模型的合理性，即模型生成的数据是否与真实数据一致。  \n5. **诊断和可视化**：在R中有多种现成的包可以对 Stan 的结果进行可视化。例如用户可以使用`bayesplot`绘制后验分布、采样轨迹、散点图等；`summary()` 函数可以总结后验统计量，包括均值、标准差、HPDI 等，帮助用户快速了解模型效果。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"6BB0E2610BE240818B8BBCCC1473C205","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"使用 Stan 进行贝叶斯建模通常包括以下步骤（以beta-binomial模型进行演示）：  \n\n（1）使用stan语法定义模型；  \n（2）使用R或其他语言调用stan和模型并进行后验采样。  \n"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0EEED1A5F34F4C6798C64B4E9F4EBED6","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"## A Beta-Binomial example in Stan  \n\n如之前的课程，假如有一个随机点运动任务的实验，每个试验中参与者判断正确的概率用 $\\pi$ 表示。  \n\n**模型假设**  \n\n- 假定参与者判断正确的概率 $\\pi$ 是从 **Beta 分布**中抽样的：  \n\n$$  \n\\begin{equation}  \n\\pi \\sim \\text{Beta}(\\alpha, \\beta)  \n\\end{equation}  \n$$  \n\n- 在每次试验中，参与者的成功次数 $Y$ 服从一个 **Binomial分布**：  \n\n$$  \n\\begin{equation}  \nY \\sim \\text{Binomial}(n, \\pi)  \n\\end{equation}  \n$$  \n\n其中，$n$是试验的总次数，$Y$是成功次数。  "},{"cell_type":"markdown","metadata":{"id":"CD4CA300F35541EE96D42425CCE6A6A5","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"**模型设定**  \n\n在这个例子中，可使用Beta-Binomial 模型来表示：  \n\n> 先验分布为：$\\pi    \\sim \\text{Beta}(2, 2)$  \n> 似然函数为：$Y|\\pi  \\sim \\text{Bin}(10, \\pi)$  \n> 总试验数为10，成功次数为9 $(Y = 9)$  \n\n接下来，使用 Stan 来表达和设定 Beta-Binomial 模型："},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"4D353F3EBB16470F93B1E8D073DDC0D3","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 使用Stan语法建构模型\nstan_model_code <- \"\ndata {  //数据块\n  int<lower=0> n;           // 试验次数\n  int<lower=0, upper=n> Y;  // 成功次数\n}\n\nparameters {  //参数块\n  real<lower=0, upper=1> pi;    // 成功概率参数\n}\n\nmodel {  //模型块\n  // 设置先验\n  pi ~ beta(2, 2);\n  \n  // 设置似然\n  Y ~ binomial(n, pi);\n}\n\"\n","outputs":[],"execution_count":14},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"17EADF2BAFCB4955BA8272C74ABA236D","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"在Stan语法中，定义模型通常包含了3个代码块：  \n\n**数据块`data{ }`**  \n   - 用于定义模型所需的数据类型和约束条件。  \n   - `int<lower=0> n`：定义$n$为一个整数（int）变量 ；`lower`代表变量的下界，即这个变量必须大于或等于0。  \n   - `int<lower=0, upper=n> Y`：定义Y为整数变量 ；`upper`代表变量的上界，因此此处变量的取值必须在 0 到 n 之间。  \n   - 除`int`整数外，还可以：  \n      - 用`real`定义浮点数组，代表实数;  \n      - 用`vector`定义向量，也代表实数，与real不同的是它具有一些内置属性和函数，可直接用于概率分布；  \n      - 用`matrix[n,n] ...` 定义n * n的矩阵，也就是有 n 行和 n 列的二维数组。  \n\n**参数块`parameters{ }`**  \n   - 用于定义模型的未知参数。  \n   - `real<lower=0, upper=1> pi`：定义 $\\pi$为实数，取值范围为0到1。  \n\n**模型块`model{ }`**  \n   - 用于定义先验分布和似然函数。  \n   - `pi ~ beta(2, 2)`: 定义$\\pi \\sim beta(2, 2)$ 的先验分布；  \n   - `Y ~ binomial(n, pi)`: 定义$Y \\sim binomial(n, \\pi)$的似然函数。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"BBEF4A5FBFDA45ED8143C9AF9B503259","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 将模型与真实数据结合来对后验进行采样  \n\n在以下例子中，将 MCMC 采样方法得到的参数样本定义为 `trace`。  \n- 使用rstan包中的 `stan` 函数进行 MCMC 采样模拟过程。  \n- 设置参数 `iter` 来控制每个 MCMC 链采样的次数；另外还可以通过 `warmup` 来设置热身采样次数，此阶段的样本不用于最终统计推断，但有助于提高后续采样的效率与稳定性。  \n- `chains` 表示同时运行几条MCMC链。  "},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":true,"tags":[],"slideshow":{"slide_type":"slide"},"id":"3E3B24240346422793151DD3924231BD","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 准备数据\nstan_data <- list(n = 10,Y = 9)\n\n# 拟合模型\ntrace <- rstan::stan(\n  model_code = stan_model_code,      # 定义的模型或模型文件路径\n  data = stan_data,                  # 输入数据\n  chains = 2,                        # 马尔可夫链数量\n  iter = 2000,                       # 总迭代次数（每个链）\n  warmup = 1000,                     # 热身迭代次数（不保存）\n  seed = 202409\n)","outputs":[{"output_type":"stream","name":"stdout","text":"\nSAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).\nChain 1: \nChain 1: Gradient evaluation took 5e-06 seconds\nChain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.\nChain 1: Adjust your expectations accordingly!\nChain 1: \nChain 1: \nChain 1: Iteration:    1 / 2000 [  0%]  (Warmup)\nChain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)\nChain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)\nChain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)\nChain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)\nChain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)\nChain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)\nChain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)\nChain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)\nChain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)\nChain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)\nChain 1: Iteration: 2000 / 2000 [100%]  (Sampling)\nChain 1: \nChain 1:  Elapsed Time: 0.004 seconds (Warm-up)\nChain 1:                0.003 seconds (Sampling)\nChain 1:                0.007 seconds (Total)\nChain 1: \n\nSAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).\nChain 2: \nChain 2: Gradient evaluation took 2e-06 seconds\nChain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.02 seconds.\nChain 2: Adjust your expectations accordingly!\nChain 2: \nChain 2: \nChain 2: Iteration:    1 / 2000 [  0%]  (Warmup)\nChain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)\nChain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)\nChain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)\nChain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)\nChain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)\nChain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)\nChain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)\nChain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)\nChain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)\nChain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)\nChain 2: Iteration: 2000 / 2000 [100%]  (Sampling)\nChain 2: \nChain 2:  Elapsed Time: 0.004 seconds (Warm-up)\nChain 2:                0.004 seconds (Sampling)\nChain 2:                0.008 seconds (Total)\nChain 2: \n"}],"execution_count":15},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"F0487C04E961445E9D42F7419080D6C3","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"我们可以使用ggplot2和rstan中的traceplot函数来可视化该结果  \n- 左图为参数分布图  \n- 右图为 trace 图，代表随着采样的进行(即x轴1-5000次采样)，每个参数值的大小(即y轴为每个采样参数的大小)。"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0D386029632648728E3181AF8BEDAA04","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 创建绘图数据框\nidata <- rstan::extract(trace)       # 提取后验数据\nsample_pi <- as.data.frame(idata$pi)\n\n#采样密度图\ndens_pi <- bayesplot::mcmc_dens(sample_pi) +    \n  ggplot2::labs(x = \"pi\", y = \"density\") +\n  papaja::theme_apa()\n  \n# 绘制轨迹图\ntrace_pi <- rstan::traceplot(trace,color = '#6497b1')\n\ndens_pi + trace_pi","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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askHehxa7l4gxC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\ndhLtKhjGr/AadN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src=\"https://cdn.kesci.com/upload/rt/0D386029632648728E3181AF8BEDAA04/t4h8u3ckml.svg\">"},"metadata":{"image/png":{"width":960,"height":420},"image/jpeg":{"width":960,"height":420},"image/svg+xml":{"width":960,"height":420,"isolated":true},"application/pdf":{"width":960,"height":420}}}],"execution_count":16},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"5ADBBA5125434D009763BB251115B658","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 采样的时间进程  \n\n下图展示了第一条Makov链的前20个采样结果和前200个结果  \n"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0F40C156EDE84EB09FC6FDD3D3194575","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"# 选取第一条Makov链的前20个采样结果和前200个结果\nsample_pi_20 <- as.data.frame(sample_pi[1:20, ])\nsample_pi_200 <- as.data.frame(sample_pi[1:200, ])\n\n# 绘图\noptions(repr.plot.width=16, repr.plot.height=5) \n#前20\ndens_20 <- bayesplot::mcmc_dens(sample_pi_20) +    \n        ggplot2::labs(x = \"pi\", y = \"density\") +\n        papaja::theme_apa()\ntrace_20 <- bayesplot::mcmc_trace(sample_pi_20) +  \n        ggplot2::labs(x = \"pi\", y = NULL) +\n        papaja::theme_apa() \ndens_20 + trace_20\n\n#前200\ndens_200 <- bayesplot::mcmc_dens(sample_pi_200) +    \n        ggplot2::labs(x = \"pi\", y = \"density\") +\n        papaja::theme_apa()\ntrace_200 <- bayesplot::mcmc_trace(sample_pi_200) +  \n        ggplot2::labs(x = \"pi\", y = NULL) +\n        papaja::theme_apa() \ndens_200 + trace_200","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without title","application/pdf":"JVBERi0xLjcKJbXtrvsKNCAwIG9iago8PCAvTGVuZ3RoIDUgMCBSCiAgIC9GaWx0ZXIgL0Zs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\nYLOWVcoEpzZXYgjw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vczdUClL+qBOFA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\nNTk2MgolJUVPRgo=","text/html":"<img src=\"https://cdn.kesci.com/upload/rt/0F40C156EDE84EB09FC6FDD3D3194575/t4h8u8yt84.svg\">"},"metadata":{"image/png":{"width":960,"height":300},"image/jpeg":{"width":960,"height":300},"image/svg+xml":{"width":960,"height":300,"isolated":true},"application/pdf":{"width":960,"height":300}}}],"execution_count":17},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"7D835ECE4318447C988D0B142CA3837D","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"rbind(head(sample_pi, 5), tail(sample_pi, 5))","outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 10 × 1</caption>\n<thead>\n\t<tr><th></th><th scope=col>idata$pi</th></tr>\n\t<tr><th></th><th scope=col>&lt;dbl&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>0.8798852</td></tr>\n\t<tr><th scope=row>2</th><td>0.8481490</td></tr>\n\t<tr><th scope=row>3</th><td>0.8313225</td></tr>\n\t<tr><th scope=row>4</th><td>0.7031714</td></tr>\n\t<tr><th scope=row>5</th><td>0.6596684</td></tr>\n\t<tr><th scope=row>1996</th><td>0.8655974</td></tr>\n\t<tr><th scope=row>1997</th><td>0.5120725</td></tr>\n\t<tr><th scope=row>1998</th><td>0.8568566</td></tr>\n\t<tr><th scope=row>1999</th><td>0.8538035</td></tr>\n\t<tr><th scope=row>2000</th><td>0.5416726</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 10 × 1\n\n| <!--/--> | idata$pi &lt;dbl&gt; |\n|---|---|\n| 1 | 0.8798852 |\n| 2 | 0.8481490 |\n| 3 | 0.8313225 |\n| 4 | 0.7031714 |\n| 5 | 0.6596684 |\n| 1996 | 0.8655974 |\n| 1997 | 0.5120725 |\n| 1998 | 0.8568566 |\n| 1999 | 0.8538035 |\n| 2000 | 0.5416726 |\n\n","text/latex":"A data.frame: 10 × 1\n\\begin{tabular}{r|l}\n  & idata\\$pi\\\\\n  & <dbl>\\\\\n\\hline\n\t1 & 0.8798852\\\\\n\t2 & 0.8481490\\\\\n\t3 & 0.8313225\\\\\n\t4 & 0.7031714\\\\\n\t5 & 0.6596684\\\\\n\t1996 & 0.8655974\\\\\n\t1997 & 0.5120725\\\\\n\t1998 & 0.8568566\\\\\n\t1999 & 0.8538035\\\\\n\t2000 & 0.5416726\\\\\n\\end{tabular}\n","text/plain":"     idata$pi \n1    0.8798852\n2    0.8481490\n3    0.8313225\n4    0.7031714\n5    0.6596684\n1996 0.8655974\n1997 0.5120725\n1998 0.8568566\n1999 0.8538035\n2000 0.5416726"},"metadata":{}}],"execution_count":18},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"F3E2523821664149BFA3077DD3CC3A26","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"### 采样结果可视化  \n\n* 将采样结果(5000次采样)对比真实的后验分布\\[黑线, $Beta(11, 3)$\\]  \n\n* 可以看到这个采样结果是对后验分布非常好的近似。"},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"BE7F8348D5D14214A65753C7D85F4DE7","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"x <- seq(0.2, 1, length.out = 10000)\n\n# 真实的后验分布 beta（alpha + y, beta + n - y）\ny <- dbeta(x, 11, 3)\nposterior_data <- data.frame(x = x, y = y)\n\n#绘制采样结果直方图\nhist_pi <- bayesplot::mcmc_hist(sample_pi, bins=30) +    \n        ggplot2::labs(x = \"pi\", y = \"count\") +\n        papaja::theme_apa()\n\n#绘制采样结果分布图和真实后验分布图\ndens_pi_mix <- bayesplot::mcmc_dens(sample_pi) +  #采样结果\n  ggplot2::geom_line(data = posterior_data, aes(x = x, y = y), color = \"black\",size = 0.8) +  #真实后验\n  ggplot2::labs(x = \"pi\", y = \"density\") +\n  papaja::theme_apa()\n\nhist_pi + dens_pi_mix ","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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sQ16sQriO3bIYT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\nMqUfM4kecOC+kwplWLKOlqJMZ5ug9QSv8FneNgC8N3jMrw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+ZpINsac9H2wOQJ3+ezL0t/XccAhzYNmbd4uRFbcH+JESRgWjFIkLNVDdD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src=\"https://cdn.kesci.com/upload/rt/BE7F8348D5D14214A65753C7D85F4DE7/t4h8xqonhw.svg\">"},"metadata":{"image/png":{"width":960,"height":300},"image/jpeg":{"width":960,"height":300},"image/svg+xml":{"width":960,"height":300,"isolated":true},"application/pdf":{"width":960,"height":300}}}],"execution_count":19},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"0EFA0988A5EB421E83D95B6520D41854","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"## 练习  \n> 📃以**Normal-Normal模型**为例来练习使用Stan进行MCMC模拟    \n\n在lec5中，我们利用基于**Normal-Normal模型**的例子练习了网格近似法来估计参数。  \n\n接下来，我们基于 Normal-Normal 再次对平均反应时间和标准差进行推断。不过这次，我们将使用 Stan 实现 MCMC 采样，而不是网格法.  \n\n**模型设定：**  \n- 假设 $\\mu$ 是参与者在随机点运动任务中的**平均反应时间**（单位：ms）。  \n- 假设 $\\sigma$ 是参与者在随机点运动任务中的**标准差**（单位：ms）。  \n  \n**先验分布**  \n我们对参与者的反应时间有一个初步的假设：  \n- 先验分布设为正态分布，平均反应时间$\\mu$约为 300 ms，标准差 $\\sigma$ 为 50 ms。  \n- 因此， $\\mu$ 的先验分布可以表示为  \n$$  \n\\mu \\sim \\text{Normal}(300, 50)  \n$$  \n\n**观测数据**  \n- 观测数据 $Y$ 表示参与者在实验中实际的反应时间。  \n- 假设我们收集了被试完成 5 次实验的反应时间：  \n$$  \nY = [320, 310, 280, 340, 300] ms  \n$$  \n\n- 为简化问题，我们假定反应时间 $Y$ 的标准差 $\\sigma$ 是已知的，$\\sigma$ = 20 ms。  \n\n**似然模型**  \n- 观测数据 $Y_i$服从一个均值为$\\mu$、标准差为 $\\sigma$ 的正态分布：  \n\n$$  \nY_i |\\mu \\stackrel{ind}{\\sim} \\text{Normal}(\\mu, \\sigma^2)  \n\\tag{1}  \n$$  \n\n<div style=\"padding-bottom: 30px;\"></div>  "},{"cell_type":"markdown","metadata":{"id":"28B999B8C8C046E8A0FD2DB42D923551","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"**完整的贝叶斯模型即为：**  \n\n$$  \n\\begin{equation}  \n\\begin{split}  \nY_i|\\mu & \\stackrel{ind}{\\sim} \\text{Normal}(\\mu, \\sigma^2) \\\\  \n\\mu & \\sim \\text{Normal}(\\mu = 300, \\sigma^2 = 50^2)\\\\  \n\\end{split}  \n\\tag{1}  \n\\end{equation}  \n$$  \n\n<div style=\"padding-bottom: 30px;\"></div>"},{"cell_type":"code","metadata":{"collapsed":false,"id":"57B038C51B4F460FACD5698A58C7664F","jupyter":{"outputs_hidden":false},"notebookId":"68e75e68a16e086f2ca29129","slideshow":{"slide_type":"slide"},"tags":[],"scrolled":false,"trusted":true},"source":"#===========================================================================\n#                            block1: 请修改 ... 中的值。\n#===========================================================================\n\n#构建模型\n\nstan_code <- \"\ndata {\n  int<lower=0> n;           // 观测数据的数量\n  vector[n] Y;              // 观测数据\n}\n\nparameters {\n  real mu;                  // 反应时间均值\n}\n\nmodel {\n  // 先验分布\n  mu ~ normal(300, 50);\n\n  // 似然函数\n  Y ~ normal(mu, 20);\n}\n\"","outputs":[],"execution_count":1},{"cell_type":"code","metadata":{"collapsed":false,"id":"91E101E9B4084FD593A275A9D7ACFBFB","jupyter":{"outputs_hidden":false},"notebookId":"68e75e68a16e086f2ca29129","slideshow":{"slide_type":"slide"},"tags":[],"scrolled":true,"trusted":true},"source":"#===========================================================================\n#                            block2: 请修改 ... 中的值。\n#===========================================================================\n#准备数据\ndata_list <- list(\n  Y = c(320, 310, 280, 340, 300), # 观测数据\n  n = 5                          # 观测数据的数量\n)\n\ntrace <- rstan::stan(\n  model_code = stan_code,            # 定义的模型或模型文件路径\n  data = data_list,                  # 输入数据\n  chains = 4 ,                        # 马尔可夫链数量\n  iter = 2000 ,                       # 总迭代次数\n  warmup = 1000 ,                      # 热身迭代次数\n  seed = 202409\n)","outputs":[{"output_type":"stream","name":"stdout","text":"\nSAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).\nChain 1: \nChain 1: Gradient evaluation took 4e-06 seconds\nChain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.04 seconds.\nChain 1: Adjust your expectations accordingly!\nChain 1: \nChain 1: \nChain 1: Iteration:    1 / 2000 [  0%]  (Warmup)\nChain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)\nChain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)\nChain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)\nChain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)\nChain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)\nChain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)\nChain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)\nChain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)\nChain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)\nChain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)\nChain 1: Iteration: 2000 / 2000 [100%]  (Sampling)\nChain 1: \nChain 1:  Elapsed Time: 0.004 seconds (Warm-up)\nChain 1:                0.004 seconds (Sampling)\nChain 1:                0.008 seconds (Total)\nChain 1: \n\nSAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).\nChain 2: \nChain 2: Gradient evaluation took 2e-06 seconds\nChain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.02 seconds.\nChain 2: Adjust your expectations accordingly!\nChain 2: \nChain 2: \nChain 2: Iteration:    1 / 2000 [  0%]  (Warmup)\nChain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)\nChain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)\nChain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)\nChain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)\nChain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)\nChain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)\nChain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)\nChain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)\nChain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)\nChain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)\nChain 2: Iteration: 2000 / 2000 [100%]  (Sampling)\nChain 2: \nChain 2:  Elapsed Time: 0.004 seconds (Warm-up)\nChain 2:                0.003 seconds (Sampling)\nChain 2:                0.007 seconds (Total)\nChain 2: \n\nSAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).\nChain 3: \nChain 3: Gradient evaluation took 1e-06 seconds\nChain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.01 seconds.\nChain 3: Adjust your expectations accordingly!\nChain 3: \nChain 3: \nChain 3: Iteration:    1 / 2000 [  0%]  (Warmup)\nChain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)\nChain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)\nChain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)\nChain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)\nChain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)\nChain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)\nChain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)\nChain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)\nChain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)\nChain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)\nChain 3: Iteration: 2000 / 2000 [100%]  (Sampling)\nChain 3: \nChain 3:  Elapsed Time: 0.004 seconds (Warm-up)\nChain 3:                0.004 seconds (Sampling)\nChain 3:                0.008 seconds (Total)\nChain 3: \n\nSAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).\nChain 4: \nChain 4: Gradient evaluation took 1e-06 seconds\nChain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.01 seconds.\nChain 4: Adjust your expectations accordingly!\nChain 4: \nChain 4: \nChain 4: Iteration:    1 / 2000 [  0%]  (Warmup)\nChain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)\nChain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)\nChain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)\nChain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)\nChain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)\nChain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)\nChain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)\nChain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)\nChain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)\nChain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)\nChain 4: Iteration: 2000 / 2000 [100%]  (Sampling)\nChain 4: \nChain 4:  Elapsed Time: 0.004 seconds (Warm-up)\nChain 4:                0.003 seconds (Sampling)\nChain 4:                0.007 seconds (Total)\nChain 4: \n"}],"execution_count":2},{"cell_type":"code","metadata":{"id":"510A13C5668F431EAD228EB75CCEEB6E","notebookId":"68e75e68a16e086f2ca29129","jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"trusted":true},"source":"pacman::p_load(patchwork,tidyverse,rstan)","outputs":[],"execution_count":10},{"cell_type":"code","metadata":{"collapsed":false,"id":"5A260984C16240ABAD68825E31F1C3CD","jupyter":{"outputs_hidden":false},"notebookId":"68e75e68a16e086f2ca29129","slideshow":{"slide_type":"slide"},"tags":[],"scrolled":false,"trusted":true},"source":"#创建绘图数据框\nidata <- rstan::extract(trace)\nsample_mu <- as.data.frame(idata$mu)\n#采样密度图\ndens_mu <- bayesplot::mcmc_dens(sample_mu) +    \n  ggplot2::labs(x = \"mu_prior\", y = \"density\") +\n  papaja::theme_apa()\n\n# 绘制轨迹图\ntrace_mu <- rstan::traceplot(trace,color = '#6497b1')\n\ndens_mu + trace_mu","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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rcZ9co105Q8I/I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\nmudQuIeiTChffVrTC1F2VfdR7RQjzuNzZT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src=\"https://cdn.kesci.com/upload/rt/5A260984C16240ABAD68825E31F1C3CD/t4hfjq9q7r.svg\">"},"metadata":{"image/png":{"width":960,"height":360},"image/jpeg":{"width":960,"height":360},"image/svg+xml":{"width":960,"height":360,"isolated":true},"application/pdf":{"width":960,"height":360}}}],"execution_count":11},{"cell_type":"code","metadata":{"jupyter":{},"collapsed":false,"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"CC3DAEAC22A24940937C98A052319BAB","notebookId":"68e75e68a16e086f2ca29129","trusted":true},"source":"#===========================================================================\n#                            为了和真实的后验分布进行比较，计算真实的后验分布。\n#===========================================================================\n\n# 先验分布的均值和标准差\nmu_prior <- 300  # 先验均值\nsigma_prior <- 50  # 先验标准差\n\n# 观测数据的标准差 (已知)\nsigma_obs <- 20\n\n# 假设观测数据\nobserved_data <- c(320, 310, 280, 340, 300)  # 替换为实际观测数据\n\n# 计算观测数据的数量和均值\nn <- length(observed_data)  \ny_mean <- mean(observed_data)  \n\n# 计算后验分布的均值和方差\nposterior_mean <- (sigma_obs^2 * mu_prior + n * sigma_prior^2 * y_mean) / (n * sigma_prior^2 + sigma_obs^2)\nposterior_variance <- (sigma_prior^2 * sigma_obs^2) / (n * sigma_prior^2 + sigma_obs^2)\nposterior_std <- sqrt(posterior_variance)\n\n# 输出结果\ncat(\"后验分布的均值:\", posterior_mean)\ncat(\"后验分布的标准差:\", posterior_std)","outputs":[{"output_type":"stream","name":"stdout","text":"后验分布的均值: 309.6899后验分布的标准差: 8.804509"}],"execution_count":12},{"cell_type":"code","metadata":{"collapsed":false,"id":"0DBEC804A4914ED89A45C1EDA0E4BAE7","jupyter":{"outputs_hidden":false},"notebookId":"68e75e68a16e086f2ca29129","slideshow":{"slide_type":"slide"},"tags":[],"scrolled":false,"trusted":true},"source":"# 计算真实的后验分布\nx <- seq(200, 400, length.out = 5000)                     # 创建从200到400的序列\ny <- dnorm(x, mean = posterior_mean, sd = posterior_std)  # 计算后验分布的概率密度\nposterior_real <- data.frame(x = x, y = y)\n\n#绘制采样结果直方图\nhist_mu <- bayesplot::mcmc_hist(sample_mu, bins=50) +    \n        ggplot2::labs(x = \"mu\", y = \"count\") +\n        papaja::theme_apa()\n\n#绘制采样结果分布图和真实后验分布图\ndens_mu_mix <- bayesplot::mcmc_dens(sample_mu) +  #采样结果\n  ggplot2::geom_line(data = posterior_real, aes(x = x, y = y), color = \"red\",size = 0.8) +  #真实后验\n  ggplot2::labs(x = \"mu\", y = \"density\") +\n  papaja::theme_apa()\n\noptions(repr.plot.width=16, repr.plot.height=6) \nhist_mu + dens_mu_mix \n","outputs":[{"output_type":"display_data","data":{"text/plain":"plot without 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DKDN3ZAMQZKKOZ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\nIC9T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src=\"https://cdn.kesci.com/upload/rt/0DBEC804A4914ED89A45C1EDA0E4BAE7/t4hfkg4h1q.svg\">"},"metadata":{"image/png":{"width":960,"height":360},"image/jpeg":{"width":960,"height":360},"image/svg+xml":{"width":960,"height":360,"isolated":true},"application/pdf":{"width":960,"height":360}}}],"execution_count":13},{"cell_type":"markdown","metadata":{"id":"9635E7E788C84F4E9C974A19E9A3ABF2","jupyter":{},"notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":"### 总结  \n\n在本节课中，相对深入地对Metropolis-Hastings 算法进行讲解。通过 Normal-Normal 模型 的例子，演示了如何使用 MCMC 来近似后验分布。MCMC 是一种非常强大的工具，尤其在解析解无法直接求得时，提供了一种灵活且有效的计算方法。  \n\n随着模型的复杂性增加，**后验分布可能变得难以解析，甚至无法获得。** 在这种情况下，近似方法是必要的。  \n\n我们学习了两种用于逼近后验分布的技术：  \n1. **网格近似法：** 通过离散化参数空间，计算每个点的后验分布，再通过这些点近似整个后验。  \n2. **马尔科夫链蒙特卡罗（MCMC）：** 通过随机采样，生成符合后验分布的样本，逼近目标分布。  \n\n"},{"cell_type":"markdown","metadata":{"id":"0B059FB5227C4A4DAB35C1CBA026C442","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"**补充介绍：细致平衡 (detail Balance)**  \n\n从一个非后验分布的建议分布$q(x)$中采样，竟然可以得到关于参数的后验分布$p(x)$。  \n\n🤔这非常神奇，这到底是怎么做到的？  \n\n一切的关键在于，MCMC 的性质：细致平衡 (detailed balance)。  \n- 正如之前关于心情的例子一样，只要记录每天的心情，就可以得到关于心境的分布（类似于参数的**后验分布**）。  \n- 这个概率分布代表了心境的乐观水平，分布的均值越大，代表个体越乐观。  \n- 而我们在最开始记录心情之前，并不知道这个后验分布是什么形态的。  \n- 我们只是按照**转移矩阵**提供的概率转化心情。换句话说，心情受到影响后如何转化是我们确定的(建议分布)，但我们却不清楚自己的乐观程度(后验分布)。  \n- 最后需要注意的是，后验分布也**与最开始的心情无关**。无论最开始是开心还是悲伤，都不影响个体总体上乐观的心态。"},{"cell_type":"markdown","metadata":{"id":"9E2E9231C27E4DC98355C8D2492445EE","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"它的数学基础在于，当心境无限演化下去，状态转移的概率达到平衡，也就是所谓的细致平衡：  \n\n假设，状态转移矩阵为 P  \n\n| 心情 | 开心$\\theta^{(n)}_{1}$ | 冷静$\\theta^{(n)}_{2}$ | 悲伤$\\theta^{(n)}_{3}$ | ... |  \n| :----: | :----: | :----: | :----: | :----: |  \n| 开心$\\theta^{(n-1)}_{1}$ | 0.5 | 0.25 | 0.25 | ... |  \n| 冷静$\\theta^{(n-1)}_{2}$ | 0.5 | 0 | 0.5 | ... |  \n| 悲伤$\\theta^{(n-1)}_{3}$ | 0.25 | 0.25 | 0.5 | ... |  \n| ... | ... | ... | ... | ... |  \n\n假设每天记录 10000个个体的心情，我们可以用 $\\pi$ 来描述这个群体的心情分布。  \n\n- 可以想象，第二天这 10000个个体的心情可能发生变化，也就是 $\\pi * P$ (矩阵乘法)。  \n- 由于这 10000个个体的乐观程度（类似于特质）总体上不会变化，所以在总体上，他们的分布不会变化，也就是 $\\pi * P = \\pi$。  \n- 那么就会有 $\\pi(i)* P(i,j) = \\pi(j)* P(j,i)$。其中 i 代表上面矩阵的行，j代表矩阵的列。  \n\n其中，满足上述公式的 $\\pi$ 就是参数的后验分布。  \n- 然而，我们一开始并不知道 $P$。  \n- 但我们可以通过加入建议分布$q(x)$和拒绝率$\\alpha$来替代 $P$。  \n- 得到： $\\pi(i)* q(i,j) * \\alpha(i,j) = \\pi(j)* q(j, i) * \\alpha(j, i)$  \n\n也就是，我们通过建议分布产生参数*拒绝率的方式来采样模拟了P。  \n- 一个不恰当的比喻：状态转移矩阵 P 是你真实的乐观程度，但只有上帝知道你的本来面目 P。  \n- 然而，你能认识到自己当下的情绪 Q，并且在漫长人生中，你可以识别那些不属于自己的情绪 $\\alpha$ 。  \n- 最后，你对自己的认识越来越接近上帝....  \n"},{"cell_type":"markdown","metadata":{"id":"3CF9FACC572F44A48A0420B9BBC9F7A5","notebookId":"68e75e68a16e086f2ca29129","runtime":{"status":"default","execution_status":null,"is_visible":false},"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"}},"source":"最后，推荐 MCMC 讲解最好的视频(没有之一)：【蒙特卡洛（Monte Carlo, MCMC）方法的原理和应用】 https://www.bilibili.com/video/BV17D4y1o7J2/?share_source=copy_web&vd_source=4b5b4646c3f53f1b80954c381226c913  \n\n如果还是不懂 MCMC 原理，那放弃也行.....  \n\n不了解 MCMC 原理，并不影响对于它的使用。"},{"cell_type":"markdown","metadata":{"jupyter":{},"scrolled":false,"tags":[],"slideshow":{"slide_type":"slide"},"id":"CAA72F56FCBA4F0BB72F2B623185481E","runtime":{"status":"default","execution_status":null,"is_visible":false},"notebookId":"68e75e68a16e086f2ca29129"},"source":"## 附录  \n本课的Python代码与R代码为单独的代码脚本，见：https://gitee.com/hcp4715/PyBayesian"}],"metadata":{"kernelspec":{"language":"R","display_name":"R","name":"ir"},"language_info":{"codemirror_mode":"r","name":"R","mimetype":"text/x-r-source","file_extension":".r","version":"3.3.2","pygments_lexer":"r"}},"nbformat":4,"nbformat_minor":4}